Thisvolumerepresents the proceedings ofthe Fourth International Conference onTypedLambdaCalculiandApplications,TLCA'99,heldinL'Aquila,on7-9 April1999. It contains25contributions. Fiftywere submitted, their overallqualitywas high, and selection was di?cult. The Programme Committee is very grateful toeveryonewhosubmittedapaper. Italsocontainstwopapersintroducingthe "demos"of"tlcasoftware",i. e. industrialproductsmakinguseoftypedlamb- calculi. Thetutorialson - DenotationalsemanticsbyThomasEhrhardandJohnLongley,and - IntersectiontypesbyMarioCoppoandMariangiolaDezaniarenotincluded inthisvolume. Theeditor wishestothankthemembersoftheProgrammeCommitteeand theOrganizingCommitteelisted, fortheir hard work andsupport, witha s- cial mention for Benedetto Intrigila. He also thanks Corrado Boh .. m for kindly acceptingthe taskofdeliveringabanquetspeech. Theeditor alsoexpresses hisgratitude to allthereferees listed on the next page,as wellas tothose whowishnotto belisted fortheiressential assistance andtimegenerouslygiven. Marseille,January1999 Jean-YvesGirard ProgrammeCommittee S. Abramsky(Edinburgh) T. Coquand(Got .. eborg) J. -Y. Girard(Marseille)(Chair) R. Hindley(Swansea) J. -L.Krivine(Paris) J. Reynolds(Pittsburgh) S. Ronchi(Torino) A. Scedrov(Philadelphia) T. Streicher(Darmstadt) M. Takahashi(T oky o) P. Urzyczyn(Warszawa) OrganizingCommittee F. Corradini,A. Formisano,B. Intrigila,(Chair),M. -C. Meo, M. Nesi,A. Pierantonio,I. Salvo,S. Sorgi (Dip. Matematica, L'AquilaandDip. Informatica,LaSapienza, Roma) Referees Y. Akama T. Altenkirch F. Barbanera H. Barendregt O. Bastonero S. Berardi A. Berarducci C. Berline V. Bono M. Bugliesi F. Cardone G. Castagna I. Cervesato G. Chen R. Cockett A. Compagnoni M. Coppo T. Crolard P. -L. Curien V. Danos R. Davies P. DeGroote U. DeLiguoro M. Dezani R. Dickho? H. Geuvers N. Ghani P. Giannini S. Guerrini B. Harper R. Hasegawa H. Herbelin M. Hofmann K. Honda R. Jagadeesan T. Jim Y. Kameyama M. Kanovich R. Kashima Y. Kinoshita T. Kurata Y. Lafont J. Laird F. Lamarche P. B. Levy C. McBride M. Marz R. Matthes P. -A. Mellies G. Mitschke H. Nickau S. Nishizaki M. Parigot C. Paulin F. Pfenning B.